The Donnas are the baddest women in rock, and their major label debut “Spend the Night” has taken them from their home in Palo Alto, Calif., and propelled them around the world.

Their songs – sometimes cruel, sometimes funny – always have a girls-on-top attitude and a hard-rock bottom. With that formula, the Donnas have ignited international appeal, especially in the U.K., Spain, Italy and here in the States.

But their story isn’t one of overnight success.

This May, they’ll celebrate their 10th anniversary as a band – and “Spend the Night” has been preceded by four independent label releases.

Prima Donna Brett Anderson, the group’s lead vocalist, told The Post that she and her bandmates – Torry Castellano, Maya Ford and Allison Robertson, all 23 years old – believe that coming up slowly has benefited them.

“It’s important to grow at a realistic rate,” she said. “It’s how you keep your head on your shoulders, and maintain your personality and sanity.”

Although she feels the band has long since paid its dues, it wasn’t until “Spend the Night” broke last fall that the Donnas finally took off.

“We’ve been touring on buses for years, trying to get on radio, but you can’t really break onto radio or TV if you’re on an independent label,” she said.

“We were lucky, the press loved to write about us, but we couldn’t get on rock radio until we finally signed with a major.”

Tonight, the Donnas bring their party-girl pop-punk to Irving Plaza for a one-night stand.

Post: Cynics might look at an all-female rock band like the Donnas and dismiss you as a novelty act or attribute your success to a gimmick.

Anderson: I think every band has a gimmick. When your gimmick appears to be that you’re all girls, people treat it like it’s an insult, but when your gimmick is that you’re Swedish and you all wear matching suits, you’re a f – – – ing genius. Take Clinic. Nobody’s saying, “They’re cashing in on how they were born boys.” It’s like, “Clinic’s so smart, they wear hospital scrubs, where’d they ever get that idea?”

Post: Sounds like you’re a little p.o.-ed that your music is defined by your gender.

Anderson: Most people can’t help but put the word “girl” in front of band. When we get interviewed and somebody asks us how it feels to be in a girl band, I say, “What does it feel like to be a man reporter?”

Post: OK, so you’re a rock band first. Who do the Donnas owe their biggest influence debts to?

Anderson: AC/DC, Cinderella. In the early years maybe the Ramones, but now we have a fuller arena rock sound.

Post: Do the Donnas have groupies who follow you around?

Anderson: For a girl band, groupies are an urban legend. It’s not like at the end of a gig, there’s a line of hot guys with dream bodies who you get with, and the next day you say, “That was awesome – who’s next?” It just doesn’t work that way.

Post: But there are a lot of boys who go to your shows hoping to meet you. Are you single?

Anderson: I have a new boyfriend, and before that, I was with another guy for five years.

Post: But on stage, you project the image of being free and unattached.

Anderson: That’s part of the reason I broke up with my last boyfriend – he didn’t understand that. My new guy knows I love him, but when I’m on stage I’m not going to be talking about him.

Post: You and your bandmates have been together for years. Do you ever fight with each other?

Anderson: We know each other better than we know ourselves. We know when to leave each other alone and when we need each other. When we’re on the bus and one of us seems irritable, that’s when we give her space. We try not to press each other. It’s just common courtesy. We try to respect each other.

Post: Where does the respect come from?

Anderson: From knowing that everyone in the band is important, irreplaceable. When you realize that, respect is easy. And you know what? We like each other, too.

Post: How long have you known each other?

Anderson: We all met between the ages of 7 and 12. We have a lot in common, we’re friends, we have a bond. When you’ve known someone since elementary school, you relate to them differently from someone you met last year.

Post: You guys can’t fool each other, can you?

Anderson: Not really. We help each other out. We watch each other’s backs.

Post: Lots of your music are make-out songs, like “Take Me to the Back Seat.” Is your message that simple?

Anderson: In between all the stuff about making out, we’re saying to girls that they should make up their own rules and make sure they’re comfortable with them. That’s how I’ve tried to live my life.